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A belt and a wallet cost $42 while 7 belts and 4 wallets cost $213. Find the cost of a belt and a wallet.

 Apr 10, 2020
 #1
avatar+23646 
+2

"A belt and a wallet cost $42"

 

I THINK you might want the cost of a wallet and the cost of a belt.

 

b + w = 42             b = 42-w    sub this into the following eq

7b + 4w = 213

7(42-w) + 4w = 213     solve for 'w'    then sub this value into one of the equations to solve for 'b' 

 Apr 10, 2020
edited by ElectricPavlov  Apr 10, 2020
 #2
avatar+224 
+1

This can be written as a system of equations to solve.

Let b be the number of belts and w be the number of wallets.

 

b+w=42

7b+4w=213

 

Multiply the first equation by 4

4b+4w=168

Subtract this equation from the second.

 

(7b-4b)+(4w-4w)=213-168

The ws cancel out!

Now simplify.

3b=45

b=$15

This can be substituted back into the first equation

15+w=42

Subtract 15

w=$27

 

Double check to make sure these numbers work:

15+27=42, this one works

7(15)+4(27)=213 This one also works so this is the correct answer.

 Apr 10, 2020

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